User:Aura/Aura's Ideas on Functional Harmony (Part 1): Difference between revisions

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 === Basic Diatonic Function-Deriving Operations ===
-The way I see it, there are eight known operations which can be used to derive additional diatonic functions from the three basic functions listed above.
+The way I see it, there are seven known operations which can be used to derive additional diatonic functions from the three basic functions listed above.
 '''Stacking''' - The notes that are arrived at through stacking multiple instances of either 3/2 or 4/3 (or their tempered counterparts) are dubbed according to the number of instances stacked, and the nature of the notes separated by the interval being stacked.  Thus, stacking two instances of the Dominant or the Serviant results in the creation of the "Didominant" or "Diserviant" respectively.  This concept comes from the German language's way of referring to the chord built on the second scale degree of the Diatonic scale as the "Doppeldominante", which literally means "Double Dominant".
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 '''Detempering''' - These are notes that appear when the comma or subchroma that separates them from the Tonic or from one of the primary Nontonic functions are not tempered out, and often, though not always, fall within the uncanny valley of the three primary functions.
-'''Compositing''' - These notes have multiple functions due to occurring at the boundary between different functions or due to occurring in close proximity to other functions.
 == Facets Derived from Viennese Theory ==
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 '''Neutral Contramediant''' -  As per the name, this is nothing other than a neutralized Contramediant, and thus, it has the Tonic Parallel, Dominant Adjacent, Preserviant and Predominant functions that you expect from a Contramediant, but, like with the Neutral Mediant, it doesn't serve well at phrase endings, rather, its Tonic Parallel function is only appropriate during the middle of musical phrases.
-'''Subdietic''' - This is a note that occurs at intervals between roughly 48/25 above the Tonic and roughly 20 cents below the octave reduplication of the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Lead- however, there are functional differences between a Subdietic and a Lead in Bass-Up Tonality.  In Bass-Up Tonality, Subdietics are often more likely to be passing tones than Leads, and, when they’re not merely passing non-chord tones, they are often harder to approach and or follow up without creating some kind of awkward tonal disconnect, with such a disconnect being especially noticeable for intervals like [[64/33]].  Furthermore, whereas a Lead can resolve to the Tonic in part through a strong harmonic connection, a Subdietic is much more likely to do so through sheer brute force, and even these cases require a proper set-up, as otherwise, the awkward tonal disconnect between the Subdietic and the Tonic is likely to result in the Subdietic resolving back down to either the Lead or the Subtonic.  As if that weren't enough, the Subdietic also has the Antintersubiant function.
+'''Subgradient''' - This is a note that occurs at intervals between roughly 48/25 above the Tonic and roughly 20 cents below the octave reduplication of the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Lead- however, there are functional differences between a Subgradient and a Lead in Bass-Up Tonality.  In Bass-Up Tonality, Subgradients are often more likely to be passing tones than Leads, and, when they’re not merely passing non-chord tones, they are often harder to approach and or follow up without creating some kind of awkward tonal disconnect, with such a disconnect being especially noticeable for intervals like [[64/33]].  Furthermore, whereas a Lead can resolve to the Tonic in part through a strong harmonic connection, a Subgradient is much more likely to do so through sheer brute force, and even these cases require a proper set-up, as otherwise, the awkward tonal disconnect between the Subdietic and the Tonic is likely to result in the Subgradient resolving back down to either the Lead or the Subtonic.  As if that weren't enough, the Subgradient also has the Antintersubiant function.
-'''Superdietic''' - This is a note that occurs at intervals between roughly 20 cents above the Tonic and 25/24 above the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Contralead.  However, there there are a few functional differences between a Superdietic and a Contralead in Bass-Up Tonality that are worth considering.  For starters, Superdietics are often more likely to be passing tones than Contraleads, and, when they’re not merely passing non-chord tones, they are just as liable to resolve upward thought some sort of semitone-like motion to some form of Contralead, Semicontralead, or even a Supertonic, as they are to resolve downwards toward the Tonic, a property which intervals like 33/32 in particular are apt to demonstrate.  Furthermore, whereas a Contralead can resolve to the Tonic in part through a strong harmonic connection, a Superdietic is much more likely to do so through sheer brute force when such a resolution is noticeable.  As if that weren't enough, the Subdietic also has the Antinterregnant function.
+'''Supergradient''' - This is a note that occurs at intervals between roughly 20 cents above the Tonic and 25/24 above the Tonic.  These intervals tend to act as parachromatic alterations of either the Tonic, or, in Bass-Up Tonality, the Contralead.  However, there there are a few functional differences between a Supergradient and a Contralead in Bass-Up Tonality that are worth considering.  For starters, Supergradients are often more likely to be passing tones than Contraleads, and, when they’re not merely passing non-chord tones, they are just as liable to resolve upward thought some sort of semitone-like motion to some form of Contralead, Semicontralead, or even a Supertonic, as they are to resolve downwards toward the Tonic, a property which intervals like 33/32 in particular are apt to demonstrate.  Furthermore, whereas a Contralead can resolve to the Tonic in part through a strong harmonic connection, a Supergradient is much more likely to do so through sheer brute force when such a resolution is noticeable.  As if that weren't enough, the Subgradient also has the Antinterregnant function.
 === Basic Parachromatic Functions ===
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 '''Semilead''' - This is a note that occurs roughly at intervals between 1024/567 and 13/7 above the Tonic as the seventh scale degree.  Naturally, this interval functions as a sort of Dominant Parallel, though there are significant differences from both a Subtonic and a Lead.  For starters, the Semilead also has the Misodominant Parallel and Antimisoserviant functions, and furthermore, in Bass-Up Tonality, a Semilead is also likely to either resolve downwards to a Subtonic, or, upwards to either the Lead.  The [[11/6]] neutral seventh is a rather typical example of an interval with this function.
+== Composite Functions ==
+As per Flora's later analysis<ref>''Analysis on the 13-limit just intonation space: episode ii''. FloraC. Xenharmonic Wiki. </ref>, it turns out that notes on the boundaries of functional regions have multiple functions due to occurring at the boundary between different functions.
+'''Compositing''' - These notes occurring in close proximity to other functions and thus take on aspects of both of their neighbors.
 == Differences from Traditional Neo-Riemannian Theory ==